Abstract
We compute the phase diagram in the N→∞ limit for lattice RPN-1, CPN-1 and QPN-1 σ-models with the quartic action, and more generally for mixed isovector/isotensor models. We show that the N=∞ limit exhibits phase transitions that are forbidden for any finite N. We clarify the origin of these pathologies by examining the exact solution of the one-dimensional model: we find that there are complex zeros of the partition function that tend to the real axis as N→∞. We conjecture the correct phase diagram for finite N as a function of the spatial dimension d. Along the way, we prove some new correlation inequalities for a class of N-component σ-models, and we obtain some new results concerning the complex zeros of confluent hypergeometric functions.
Original language | English (US) |
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Pages (from-to) | 425-502 |
Number of pages | 78 |
Journal | Nuclear Physics B |
Volume | 601 |
Issue number | 3 |
DOIs | |
State | Published - May 14 2001 |
Keywords
- Mixed isovector/isotensor model
- Nematic liquid crystal* N→∞ limit* 1/N expansion
- Nonlinear σ -model
- RP model* CP model* QP model* N -vector model
ASJC Scopus subject areas
- Nuclear and High Energy Physics